Abstract
The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.
Highlights
The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems
We show that the measured distribution of kink pairs is Poisson binomial and that low-order cumulants scale as a universal power law with the quench time
In summary, using a trapped-ion quantum simulator we have measured the full distribution of topological defects in the quantum Ising chain, the paradigmatic model of quantum phase transitions, and characterized in detail its first three cumulants as a function of the quench rate
Summary
The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. It provides useful heuristics for the preparation of ground-state phases of matter in the laboratory, e.g., in quantum simulation and adiabatic quantum computation[10] It has spurred a wide variety of experimental efforts in superfluid helium[11,12,13], liquid crystals[14,15], convective fluids[16,17], superconducting rings[18,19,20], trapped ions[21,22,23], colloids[24], and ultracold atoms[25,26,27,28,29], to name some relevant examples. We show that the measured distribution of kink pairs is Poisson binomial and that low-order cumulants scale as a universal power law with the quench time
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